Hypothesis of Two-Dimensional Linear Equation —— Two-Dimensional Linear Vector Wave Projection Theory and Unified Solutions to Quantum Paradoxes
Jun Yan
For over a century, the Copenhagen interpretation of modern quantum mechanics has been plagued by idealistic tendencies, inconsistent fundamental logic, and the division between the microscopic and macroscopic realms. This paper proposes an original Hypothesis of Two-Dimensional Linear Equation. Grounded on all completed experiments in quantum physics, this hypothesis summarizes objective laws via inductive reasoning, without introducing unknown physical constants or unfalsifiable assumptions. Its core argument is as follows: the objective eigenstates of all material units in the universe stably reside in a two-dimensional orthogonal real linear space, and waves described by two-dimensional constant real vector functions constitute the sole ontological form. Human sensory organs and all physical detection devices are essentially one-dimensional observation systems. Constrained by dimensional barriers, they cannot fully capture two-dimensional ontological vectors and only acquire data through dimensionality reduction projection. A series of counterintuitive experimental phenomena in quantum mechanics, including the illusory wave function collapse, Schrödinger’s cat paradox, anomalous observations in double-slit interference, and abnormal correlations in Bell’s inequality, do not stem from intrinsic uncertainty of microscopic matter, nor do they involve any mechanism whereby consciousness interferes with objective physical laws. All quantum anomalies are essentially projection illusions arising when constant two-dimensional objective vector waves undergo linear dimensionality reduction in one-dimensional observation systems. This paper further clarifies that Heisenberg’s matrix mechanics is not an independent fundamental ontological theory. Its entire matrix operation structure is essentially the practical physical manifestation of the Hypothesis of Two-Dimensional Linear Equation. All observational data adopted by Heisenberg to develop matrix mechanics were wave signals generated by the free evolution of microscopic particles, with no point measurements that could trigger state collapse. From its inception, this theoretical system defined matter based on the manifestation of two-dimensional linear waves, and its mathematical expressions are formulated for one-dimensional observation. Heisenberg summarized observational data and mistook the wave manifestation of free evolution for the intrinsic properties of microscopic particles, failing to recognize that it is merely the natural presentation of two-dimensional vectors within a one-dimensional observation framework. Matrix mechanics was thereby established, laying the groundwork for the subsequent idealistic probabilistic interpretation of the Copenhagen school. This hypothesis redefines the nature of observation: any information collection inevitably leads to energy coupling. Such coupling locks the projection matrix and enforces linear dimensionality reduction from two dimensions to one dimension, which is the physical origin of the so-called "wave function collapse" in academia. Discarding redundant constructs such as Hilbert space, complex wave functions, probability waves, hidden variables and the many-worlds interpretation, this hypothesis completes all derivations solely with elementary real linear algebra and provides unified explanations for all classic quantum paradoxes. It reshapes the worldview of quantum mechanics at the fundamental level, anchors microscopic physics within the framework of objective materialism, and realizes the unification of physical laws governing microscopic particles and macroscopic entities.
•Jun 10, 2026•0 citations